This disclosure relates generally to the field of analysis of measurements made of physical characteristics of subsurface formations. More specifically, the disclosure relates to techniques for such interpretation using factor analysis.
In interpretation and analysis of “well log” measurements (i.e., measurements made by moving sensing instruments through a wellbore drilled through the formations) using techniques known in the art, a plurality of measurements each of different formation physical properties may be made and/or recorded to enable determination of the formation mineral (matrix) content and characteristics of fluids present in the formation pore spaces (porosity).
Measurement of a single property of subsurface formations, such as nuclear magnetic resonance (NMR) transverse relaxation times (T2), can yield an array, e.g., a T2 distribution, of components providing information about various fluids occupying the pore space in formations. Such measurements may be called a “one-to-many” type of measurement. Similarly, measurements of a plurality of different physical properties may be made to provide information about the same formation physical property such as the fractional volume of pore space (quantified porosity) e.g., using gamma-gamma density measurements, neutron-gamma density porosity measurements, thermal neutron porosity measurements, epithermal neutron porosity measurements, acoustic property determined porosity using compressional and shear wave acoustic data, etc., which may be called a “many-to-one” type of measurement. Both these types of measurements can be difficult to interpret or reconcile due, for example, to insufficient information about the actual fluid/matrix/formation characteristics, for instance the type and volume of fluids downhole in the case of NMR T2 distribution and the actual porosity in the case of the above example apparent porosity measurements.
Conventional interpretation workflows, such as one sold under the service mark ELAN FE, (a service mark of Schlumberger Technology Corporations, Sugar Land, Tex.) requires a priori knowledge of certain subsurface formation characteristics to set up an input parameter matrix to resolve all the input measurements simultaneously within set constraints and uncertainties to determine the fluid and matrix volumes or other desired physical properties of the formations.
A number of empirical methods are available whereby generally two or more equations using measurements related to two or more physical properties are solved simultaneously for two or more unknowns. Such methods may be implemented as computations or may be graphical, but may require some a priori knowledge of the subsurface environment and possible input parameters obtained through experience, offset wellbore information or iteration.
Consonant or “pseudo”-consonant type measurements in space or time (for example measurements made at the same time over multiple depth-of-investigation or measurements made at different times with the same depth of investigation using, e.g., logging while drilling [“LWD”] time lapse measurements or measurements made using LWD and subsequent wireline measurements) may be solved simultaneously to infer certain desired underlying fluid/matrix/formation properties. Such methods have been proven to be effective but may require additional measurements or additional time and resources to perform the same measurements at different times and/or geodetic locations. Even with such information the underlying formation characteristics are hard to fathom and interpret.
There has been some work on understanding underlying formation/fluid/matrix characteristics using such statistical techniques as principal component analysis (PCA) or independent component analysis (ICA). Such techniques may help in dimensionality reduction, for example projecting 64 component or dimensional T2 distribution data onto a six Principal Component orthogonal subspace, but the techniques themselves do not readily provide complete understanding and interpretation of the underlying formation mineral, porosity and pore fluid characteristics.
Thus, there still remains a need to better assess correct underlying formation, fluid and matrix characteristics to be able to apply any of the foregoing techniques that may require a priori information as input thereto.